Method and system for compressed sensing joint channel estimation in a cellular communications network

ABSTRACT

Methods and systems for performing compressed time domain joint channel estimation in a multi-user MIMO wireless network include receiving training signals from a plurality of users, estimating a maximum delay spread for the received data according to a coherence bandwidth of the received data, limiting the received data in the time domain to the estimated maximum delay spread, selecting and estimating an active tap from the limited data set, and subtracting a contribution of the selected active tap from the reduced data set. These steps can be repeated until the residual signal falls below a specified minimum. The network can be a C-RAN network. The training data can be SRS or DMRS data. Limiting the received data ensures that only a few significant taps are analyzed, so that the system is not under determined and can be analyzed for accurate channel estimation using any of several existing algorithms.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/668,638, titled “Method and System for Compressed Sensing JointChannel Estimation in an LTE Cellular Communications Network,” filed onAug. 3, 2017, which is a continuation of U.S. patent application Ser.No. 14/583,076, titled “Method and System for Compressed Sensing JointChannel Estimation in an LTE Cellular Communications Network,” filed onDec. 24, 2014, the entire disclosure of which is here incorporated byreference.

FIELD

The subject matter disclosed relates to telecommunications, and moreparticularly, to methods of channel estimation in a digitaltelecommunication network.

BACKGROUND

Channel estimation in a large scale Multiple Input Multiple Output(“MIMO”) system is a very challenging task because of the increaseddimensions and associated increased complexity that arises therefrom. Alarge scale multi user MIMO system includes a first plurality ofantennae at the base station in communication with one or more receiversthat can be single or multiple antenna mobile terminals.

Large scale MIMO communication can occur in cloud RAN (C-RAN) settings,where several collocated base stations are pooled together to form asingle, virtual site with many antennae, typically much more than thatnumber of users that are in communication with the site. The advantageto such a system model lies in the increased spatial dimension, wherebybase stations can use the system on the uplink to jointly detect severalusers using simple linear detection methods such as matched filter,zero-forcing, or MMSE, so long as the channel estimate is sufficientlyaccurate. Similarly, on the downlink, the large number of antennae atthe base station can be effectively used to “beam form” signals totargeted users.

Channel estimation is an important concern in this type of system. Oneapproach is to perform channel estimation jointly for a plurality ofusers. So long as the system remains determined, this approach canprovide improved channel estimation and increased efficiency as comparedto single user channel estimation. However when using joint channelestimation the system can become under-determined as the number of usersincreases, so that it becomes impossible to accurately estimate all ofthe user channels jointly using conventional channel estimationalgorithms such as block least squares.

One approach for dealing with underdetermined systems of this type is touse compressive sensing channel estimation. This approach is based onthe idea that the number of degrees of freedom of the channel matrix issmaller than its large number of free parameters, so that a sufficientlylow rank approximation of the channel matrix can be found which can beconveniently used to solve the channel estimation problem using any ofseveral existing algorithms.

Recent efforts have attempted to solve this channel estimation problemin large scale multiuser MIMO systems by exploiting a prior knowledge ofchannel sparsity that originates from assuming a finite scattering modelof the channel. However, it has been unclear how these compressedsensing channel estimation methods could be applied in a typicalcellular communications network operating according to the Long TermEvolution, (“LTE”) standard, especially when the network is operating ina C-RAN setting.

Large scale multi user MIMO is likely to be deployed within networkshaving a C-RAN architecture and operating according to the LTE standard.In this this type of architecture, the LTE systems are likely to bebased on time division duplex (“TDD”) communication. In TDD LTE systems,channel state information is estimated in the uplink based on SoundingReference Signal (“SRS”) training signals that are included in theuplink specifically for this purpose. Estimated channel reciprocity isthen used to perform linear beam forming or precoding on the downlink.Using a comb pattern and careful cell ID selection, a relatively largenumber of users can be multiplexed to send SRS training signals in theuplink on the same sub-frame, as is required for large scale multi userMIMO communication.

As in many other wireless network environments, time domain least squarejoint channel estimation will be able to provide sufficiently accuratechannel estimation for multi user MIMO LTE networks so long as thenumber of users remains less than the number of training signalobservations. However, as the number of users in the system becomes morethan the number of observations, the system will become undetermined,and the training matrix will become ill-conditioned. The result will bepoor joint channel estimation, which will significantly impair theperformance of the downlink beam forming and precoding that are based onthe reciprocal of the channel estimations.

What is needed, therefore, is a method and system for implementingcompressed sensing joint channel estimation in a multi user MIMO LTEnetwork.

SUMMARY

Accordingly, a method and system are described for implementingcompressed sensing joint channel estimation in a multi user MIMOnetwork. The method includes estimating a maximum delay spread forreceived training signals, and limiting the received training signaldata in a time domain according to the estimated maximum delay spread,thereby limiting the active tap search space. Compressive sensing isthen applied, so that the time-limited training signal data is not underdetermined, and can be analyzed for accurate channel estimation usingany of several existing algorithms.

According to an exemplary embodiment, a method is described ofperforming time domain channel estimation in a multi-user multiple inputmultiple output (“MIMO”) wireless network. The method includes receivingdata corresponding to transmission of training signals from a pluralityof users to a base station over a MIMO wireless network, estimating amaximum delay spread for the received data according to a coherencebandwidth of the received data, determining a limited data set bylimiting the received data in a time domain according to the estimatedmaximum delay spread, selecting and estimating an active tap from thelimited data set, and subtracting a contribution of the selected activetap from the limited data set.

In some exemplary embodiments, the steps of selecting and estimating anactive tap from the limited data set and subtracting a contribution ofthe selected active tap from the reduced data set is repeated until theresidual signal norm falls below a specified minimum. And in variousexemplary embodiments, a plurality of active taps are selected.

According to another exemplary embodiment, a system is described forperforming time domain channel estimation in a multi-user multiple inputmultiple output (“MIMO”) wireless network. The system includes a signalreceiving unit configured to receive data corresponding to transmissionof training signals from a plurality of users to a base station over aMIMO wireless network, and a signal processing unit configured toestimate a maximum delay spread for the received data according to acoherence bandwidth of the received data, determine a limited data setby limiting the received data in a time domain according to theestimated maximum delay spread, select and estimate an active tap fromthe limited data set, and subtract a contribution of the selected activetap from the reduced data set.

In some exemplary embodiments, the signal processing unit is configuredto repeatedly subtract contributions of selected active taps from thereduced data set until the residual signal norm falls below a specifiedminimum. And in various exemplary embodiments, the signal processingunit is configured to select a plurality of active taps.

According to yet another exemplary embodiment, a non-transitory computerreadable medium storing a computer program is described, the computerprogram being executable by a machine for performing time domain channelestimation in a multi-user multiple input multiple output (“MIMO”)wireless network. The computer program includes executable instructionsfor receiving data corresponding to transmission of training signalsfrom a plurality of users to a base station over a MIMO wirelessnetwork, estimating a maximum delay spread for the received dataaccording to a coherence bandwidth of the received data, determining alimited data set by limiting the received data in a time domainaccording to the estimated maximum delay spread, selecting andestimating an active tap from the limited data set, and subtracting acontribution of the selected active tap from the reduced data set.

The features and advantages described herein are not all-inclusive and,in particular, many additional features and advantages will be apparentto one of ordinary skill in the art in view of the drawings,specification, and claims. Moreover, it should be noted that thelanguage used in the specification has been principally selected forreadability and instructional purposes, and not to limit the scope ofthe inventive subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings provide visual representations which will beused to more fully describe the representative embodiments disclosedhere and can be used by those skilled in the art to better understandthem and their inherent advantages. In these drawings, like referencenumerals identify corresponding elements, and:

FIG. 1 is a graph showing a typical group of actual channel taps and theresulting SRS training signal as they might appear in the time domaindue to discrete physical scattering of the SRS training signals;

FIG. 2 is a flow diagram illustrating steps in an embodiment of thedisclosed invention; and

FIG. 3 is a block diagram illustrating an embodiment of the disclosedsystem.

DETAILED DESCRIPTION

A method and system are described for implementing compressed sensingjoint channel estimation of all the desired users (and interferers, ifrequired) in a multi user MIMO network.

As noted above, frequency domain channel estimation is typically unableto fully capture the frequency selectivity of the channel because itlacks the required degrees of freedom due to the limited number ofcarriers that can be observed. Instead, the method and system describedherein estimates the positions of only a small number of significantchannel taps in the time domain for each user. In this way, the methodessentially turns the underdetermined system into a stable, determinedsystem where existing, robust algorithms such as L1-norm or L2-normminimization-based equation solving can be applied to perform jointchannel estimation.

With reference to FIG. 1, one important aspect of the disclosed methodis estimation 104 from the received SRS signal 100 of the active channeltaps 102 for each of the users, so that the sparsity of the multiuseruplink channel can be exploited to obtain robust channel estimates fromtraining signals. Note that, while the description provided hereintypically refers to the use of SRS signals for said estimation, it willbe understood by those of ordinary skill in the art that the methoddescribed herein can also be applied to DMRS training signals.

In FIG. 1, a typical group of actual channel taps 102, and the resultingSRS training signal 100 as it is received by the base station, are shownas they might appear in the time domain due to discrete physicalscattering of the SRS training signals. Compressed sensing-based channelestimation essentially detects the positions of the active channel taps,and then estimates them 104 using a channel matrix model that has a verylow rank compared to the observation 100.

With reference to FIG. 2, in exemplary embodiments the following stepsare performed:

Step 1: From the received 200 training signal data 100, using anestimate 202 of the maximum delay spread 106, and assuming a cyclicnature of the channel due to the properties of the Fourier transform, alimited data set for each user is determined 204 by considering only thetraining sample data 100 that falls within the maximum delay spread 106and cyclic extensions thereof. Using only training sample data that isreceived during the maximum delay spread 106 is justified, because themaximum delay spread 106 can be estimated with reasonable accuracy fromthe coherence bandwidth of the received signal training 100. In this waythe channel sparsity is well characterized inherently by the reduced setof time domain training samples 100, even though the exact channelsparsity for each user is not explicitly known.

Step 2: Using the reduced set of training signal data 100, active tapselection is performed using orthogonal matching pursuit, basis pursuit,or another, similar algorithm that selects 206 the active taps 102 bydetermining the time domain training sample that is most closelycorrelated in magnitude with the observed signal 100, and then estimates208 an active channel tap 102 using existing l1-norm or l2-normminimization methods. The contribution of the selected, active channeltap 102 is then subtracted 210 from the received signal 100, so thatonly a residual signal remains.

Step 3: The process described in step 2 is repeated 212 by applying itto the residual signal to identify and estimate an additional activechannel tap, and to re-estimate all previously estimated and currentlyestimated active channel taps from the original received data.

In embodiments, Step 3 is repeated until all of the active taps of allthe users in the received signals have been estimated, resulting in aresidual signal norm that is smaller than a specified minimum value 214.In some embodiments, the process is made more efficient by grouping aplurality of the most strongly correlated channel taps and estimatingthem jointly, removing the contributions of all the taps in the groupfrom the received data, and then repeat the process until all of theactive taps have been estimated. It should be noted that not all of theactive taps for all of the users will necessarily be time-aligned.

In embodiments, any of several l1-norm minimization methods withadjustable de-noising functions is used in the above process. Thesealgorithms (e.g. NESTA or LASSO) inherently exploit the channel sparsityby iteratively solving a smoothed version of an l1-norm objectivefunction that is constructed by parametric de-noising of an originall1-norm objective. Several classes of interior-point methods, which areof polynomial complexity, can then be applied to produce a solution.

It should be noted that the disclosed method exploits the channelsparsity implicitly, by estimating the significant channel taps over areduced data set and by stopping the search after the power norm of theresidual signal falls below a pre-determined threshold. For this reason,there is no need in the present method for prior knowledge of thechannel sparsity. This is an advantageous feature of the present method,especially when it is applied to an LTE based C-RAN wirelesscommunication network.

It should also be noted that the methods disclosed herein can be appliedto determined and over-determined systems, although they may tend to beinherently more complex than typically applied methods. For this reason,application of the present methods to under-determined systems, such aslarge scale multi-user MIMO systems, is emphasized herein, because ofthe present method's ability to provide a performance advantage byexploiting the structure of the received training signals, and inparticular by exploiting the channel sparsity contained in the trainingsignals.

With reference to FIG. 3, the system disclosed herein 300 includes asignal receiving unit 302 in communication with at least one antenna 304and configured to receive training signals from a plurality of users,and a signal processing unit 306 configured to estimate a maximum delayspread for the received data according to a coherence bandwidth of thereceived data, determine a limited data set by limiting the receiveddata in a time domain according to the estimated maximum delay spread,select and estimate an active tap from the limited data set, andsubtract a contribution of the selected active tap from the reduced dataset.

The signal processing unit 306 is an instruction execution machine,apparatus, or device and may comprise one or more of a microprocessor, adigital signal processor, a graphics processing unit, an applicationspecific integrated circuit (ASIC), a field programmable gate array(FPGA), and the like. The signal processing unit 306 may be configuredto execute program instructions stored in a memory and/or data storage(both not shown). The memory may include read only memory (ROM) andrandom access memory (RAM). The data storage may include a flash memorydata storage device for reading from and writing to flash memory, a harddisk drive for reading from and writing to a hard disk, a magnetic diskdrive for reading from or writing to a removable magnetic disk, and/oran optical disk drive for reading from or writing to a removable opticaldisk such as a CD ROM, DVD or other optical media. The drives and theirassociated computer-readable media provide nonvolatile storage ofcomputer readable instructions, data structures, program modules andother data.

It is noted that the methods described herein can be embodied inexecutable instructions stored in a computer readable medium for use byor in connection with an instruction execution machine, apparatus, ordevice, such as a computer-based or processor-containing machine,apparatus, or device. It will be appreciated by those skilled in the artthat for some embodiments, other types of computer readable media may beused which can store data that is accessible by a computer, such asmagnetic cassettes, flash memory cards, digital video disks, Bernoullicartridges, RAM, ROM, and the like may also be used in the exemplaryoperating environment. As used here, a “computer-readable medium” caninclude one or more of any suitable media for storing the executableinstructions of a computer program in one or more of an electronic,magnetic, optical, and electromagnetic format, such that the instructionexecution machine, system, apparatus, or device can read (or fetch) theinstructions from the computer readable medium and execute theinstructions for carrying out the described methods. A non-exhaustivelist of conventional exemplary computer readable medium includes: aportable computer diskette; a RAM; a ROM; an erasable programmable readonly memory (EPROM or flash memory); optical storage devices, includinga portable compact disc (CD), a portable digital video disc (DVD), ahigh definition DVD (HD-DVD™), a BLU-RAY disc; and the like.

The signal processing unit 306 and signal receiving unit 302 preferablydetect and analyze transmissions from at least one or more remote nodesthat operate in a networked environment using logical connections to oneor more base stations (“BS's”). The remote node may be another BS, auser equipment (“UE”), a computer, a server, a router, a peer device orother common network node. The base station may interface with awireless network and/or a wired network. For example, wirelesscommunications networks can include, but are not limited to, CodeDivision Multiple Access (CDMA), Time Division Multiple Access (TDMA),Frequency Division Multiple Access (FDMA), Orthogonal Frequency DivisionMultiple Access (OFDMA), and Single-Carrier Frequency Division MultipleAccess (SC-FDMA). A CDMA network may implement a radio technology suchas Universal Terrestrial Radio Access (UTRA), TelecommunicationsIndustry Association's (TIA's) CDMA2000®, and the like. The UTRAtechnology includes Wideband CDMA (WCDMA), and other variants of CDMA.The CDMA2000® technology includes the IS-2000, IS-95, and IS-856standards from The Electronics Industry Alliance (EIA), and TIA. A TDMAnetwork may implement a radio technology such as Global System forMobile Communications (GSM). An OFDMA network may implement a radiotechnology such as Evolved UTRA (E-UTRA), Ultra Mobile Broadband (UMB),IEEE 802.11 (Wi-Fi), IEEE 802.16 (WiMAX), IEEE 802.20, Flash-OFDMA, andthe like. The UTRA and E-UTRA technologies are part of Universal MobileTelecommunication System (UMTS). 3GPP Long Term Evolution (LTE) andLTE-Advance (LTE-A) are newer releases of the UMTS that use E-UTRA.UTRA, E-UTRA, UMTS, LTE, LTE-A, and GAM are described in documents froman organization called the “3rd Generation Partnership Project” (3GPP).CDMA2000® and UMB are described in documents from an organization calledthe “3rd Generation Partnership Project 2” (3GPP2). The techniquesdescribed herein may be used for the wireless networks and radio accesstechnologies mentioned above, as well as other wireless networks andradio access technologies. Other examples of wireless networks include,for example, a BLUETOOTH network, a wireless personal area network, anda wireless 802.11 local area network (LAN).

Examples of wired networks include, for example, a LAN, a fiber opticnetwork, a wired personal area network, a telephony network, and/or awide area network (WAN). Such networking environments are commonplace inintranets, the Internet, offices, enterprise-wide computer networks andthe like. In some embodiments, signal processing unit 306 may includelogic configured to support direct memory access (DMA) transfers betweenmemory and other devices.

It should be understood that the arrangement illustrated in FIG. 3 isbut one possible implementation and that other arrangements arepossible. It should also be understood that the various systemcomponents (and means) defined by the claims, described above, andillustrated in the various block diagrams represent logical componentsthat are configured to perform the functionality described herein. Forexample, one or more of these system components (and means) can berealized, in whole or in part, by at least some of the componentsillustrated in the arrangement of hardware device 300. In addition,while at least one of these components are implemented at leastpartially as an electronic hardware component, and therefore constitutesa machine, the other components may be implemented in software,hardware, or a combination of software and hardware. More particularly,at least one component defined by the claims is implemented at leastpartially as an electronic hardware component, such as an instructionexecution machine (e.g., a processor-based or processor-containingmachine) and/or as specialized circuits or circuitry (e.g., discretelogic gates interconnected to perform a specialized function), such asthose illustrated in FIG. 3. Other components may be implemented insoftware, hardware, or a combination of software and hardware. Moreover,some or all of these other components may be combined, some may beomitted altogether, and additional components can be added while stillachieving the functionality described herein. Thus, the subject matterdescribed herein can be embodied in many different variations, and allsuch variations are contemplated to be within the scope of what isclaimed.

In the description above, the subject matter is described with referenceto acts and symbolic representations of operations that are performed byone or more devices, unless indicated otherwise. As such, it will beunderstood that such acts and operations, which are at times referred toas being computer-executed, include the manipulation by the processingunit of data in a structured form. This manipulation transforms the dataor maintains it at locations in the memory system of the computer, whichreconfigures or otherwise alters the operation of the device in a mannerwell understood by those skilled in the art. The data structures wheredata is maintained are physical locations of the memory that haveparticular properties defined by the format of the data. However, whilethe subject matter is being described in the foregoing context, it isnot meant to be limiting as those of skill in the art will appreciatethat various of the acts and operation described hereinafter may also beimplemented in hardware.

To facilitate an understanding of the subject matter disclosed, manyaspects are described in terms of sequences of actions. At least one ofthese aspects defined by the claims is performed by an electronichardware component. For example, it will be recognized that the variousactions can be performed by specialized circuits or circuitry, byprogram instructions being executed by one or more processors, or by acombination of both. The description herein of any sequence of actionsis not intended to imply that the specific order described forperforming that sequence must be followed. All methods described hereincan be performed in any suitable order unless otherwise indicated hereinor otherwise clearly contradicted by context.

The use of the terms “a” and “an” and “the” and similar referents in thecontext of describing the subject matter (particularly in the context ofthe following claims) are to be construed to cover both the singular andthe plural, unless otherwise indicated herein or clearly contradicted bycontext. Recitation of ranges of values herein are merely intended toserve as a shorthand method of referring individually to each separatevalue falling within the range, unless otherwise indicated herein, andeach separate value is incorporated into the specification as if it wereindividually recited herein. Furthermore, the foregoing description isfor the purpose of illustration only, and not for the purpose oflimitation, as the scope of protection sought is defined by the claimsas set forth hereinafter together with any equivalents thereof entitledto. The use of any and all examples, or exemplary language (e.g., “suchas”) provided herein, is intended merely to better illustrate thesubject matter and does not pose a limitation on the scope of thesubject matter unless otherwise claimed. The use of the term “based on”and other like phrases indicating a condition for bringing about aresult, both in the claims and in the written description, is notintended to foreclose any other conditions that bring about that result.No language in the specification should be construed as indicating anynon-claimed element as essential to the practice of the invention asclaimed.

Preferred embodiments are described herein, including the best modeknown to the inventor for carrying out the claimed subject matter. Oneof ordinary skill in the art should appreciate after learning theteachings related to the claimed subject matter contained in theforegoing description that variations of those preferred embodiments maybecome apparent to those of ordinary skill in the art upon reading theforegoing description. The inventor intends that the claimed subjectmatter may be practiced otherwise than as specifically described herein.Accordingly, this claimed subject matter includes all modifications andequivalents of the subject matter recited in the claims appended heretoas permitted by applicable law. Moreover, any combination of theabove-described elements in all possible variations thereof isencompassed unless otherwise indicated herein or otherwise clearlycontradicted by context.

We claim:
 1. A method of performing time domain channel estimation in amulti-user multiple input multiple output (“MIMO”) wireless network, themethod comprising: receiving data corresponding to transmission oftraining signals from a plurality of users to a base station over a MIMOwireless network; estimating a maximum delay spread for the receiveddata according to a coherence bandwidth of the received data;determining a limited data set by limiting the received data in a timedomain according to the estimated maximum delay spread; selecting anactive tap from the limited data set; determining a number of activetaps in the MIMO multi-user wireless network; forming a well-conditionedlow rank training matrix by identifying a channel model; estimating theactive tap from the formed well-conditioned low rank training matrix;and subtracting a contribution of the selected active tap from thelimited data set.
 2. The method of claim 1, further comprising repeatingthe steps of selecting and subtracting until a residual signal normfalls below a specified minimum.
 3. The method of claim 1, wherein atleast one of the training signals is a sounding reference signal (“SRS”)signal.
 4. The method of claim 1, wherein at least one of the trainingsignals is a demodulation reference signal (“DMRS”) signal.
 5. Themethod of claim 1, wherein the MIMO wireless network is a cloud radioaccess network (“C-RAN”) network.
 6. The method of claim 1, wherein thenetwork operates using at least one of time division duplexed (“TDD”)and frequency division duplexed (“FDD”) communications.
 7. The method ofclaim 1, wherein the active tap is selected by at least one oforthogonal matching pursuit and basis pursuit.
 8. The method of claim 1,wherein the selected active tap is estimated using at least one of:l1-norm minimization; l2-norm minimization; regulated L2-normimmunization; OMP greedy matching pursuit; and stomp greedy matchingpursuit.
 9. The method of claim 1, wherein selecting an active tapincludes selecting a plurality of active taps.
 10. The method of claim9, wherein the plurality of active taps is selected according to whichactive taps have the strongest correlation to the received trainingsignal.
 11. The method of claim 9, wherein for each user the pluralityof active taps includes at least one active tap corresponding to thatuser.
 12. The method of claim 1, wherein selecting an active tap fromthe limited data set comprises: detecting active tap locations of thereduced data set; and selecting the active tap according to theestimated active tap locations.
 13. The method of claim 12, wherein theactive tap locations are detected using a matching pursuit algorithm.14. The method of claim 12, wherein the active tap is selected bysolving a l1/l2 norm minimization problem.
 15. The method of claim 1,wherein selecting an active tap from the limited data set comprisesapplying a basis pursuit de-noising function associated with an l1-normobjective function to the reduced data set.
 16. A system for performingtime domain channel estimation in a multi-user multiple input multipleoutput (“MIMO”) wireless network, the system comprising: a signalreceiving unit configured to receive data corresponding to transmissionof training signals from a plurality of users to a base station over aMIMO wireless network; and a signal processing unit configured toestimate a maximum delay spread for the received data according to acoherence bandwidth of the received data, determine a limited data setby limiting the received data in a time domain according to theestimated maximum delay spread, select an active tap from the limiteddata set, determine a number of active taps in the MIMO multi-userwireless network, form a well-conditioned low rank training matrix byidentifying a channel model, estimate the active tap from the formedwell-conditioned low rank training matrix, and subtract a contributionof the selected active tap from the limited data set.
 17. The system ofclaim 16, wherein the signal processing unit is further configured torepeatedly select the active tap and subtract the contribution until aresidual signal norm falls below a specified minimum.
 18. The system ofclaim 16, wherein at least one of the training signals is a soundingreference signal (“SRS”) signal.
 19. The system of claim 16, wherein atleast one of the training signals is a demodulation reference signal(“DMRS”) signal.
 20. The system of claim 16, wherein the MIMO wirelessnetwork is a cloud radio access network (“C-RAN”) network.
 21. Thesystem of claim 16, wherein the network operates using time divisionduplexed (“TDD”) and frequency division duplexed (“FDD”) communications.22. The system of claim 16, wherein the signal processing unit isconfigured to select the active tap by at least one of orthogonalmatching pursuit and basis pursuit.
 23. The system of claim 22, whereinthe signal processing unit is further configured to select the selectedactive tap using at least one of: l1-norm minimization; l2-normminimization; regulated L2-norm immunization; OMP greedy matchingpursuit; and stomp greedy matching pursuit.
 24. The system of claim 16,wherein the signal processing unit is configured to select a pluralityof active taps.
 25. The system of claim 24, wherein the signalprocessing unit is configured to select the plurality of active tapsaccording to which active taps have the strongest correlation to thereceived training signal.
 26. The system of claim 24, wherein the signalprocessing unit is configured to select the plurality of active tapssuch that, for each user, the plurality of active taps includes at leastone active tap corresponding to that user.
 27. The system of claim 16,wherein the signal processing unit is configured to select and estimatethe active tap by: determining a number of active taps in the wirelessnetwork; identifying a channel model; forming a well-conditioned lowrank training matrix; and estimating the active tap from the low ranktraining matrix.
 28. The system of claim 16, wherein the signalprocessing unit is configured to select the active tap by: detectingactive tap locations of the reduced data set; and selecting the activetap according to the estimated active tap locations.
 29. The system ofclaim 28, wherein the signal processing unit is configured to detect theactive tap locations using a matching pursuit algorithm.
 30. The systemof claim 28, wherein the signal processing unit is configured to selectthe active tap by solving an l1/l2 norm minimization problem.
 31. Thesystem of claim 16, wherein the signal processing unit is configured toselect the active tap by applying a basis pursuit de-noising functionassociated with an l1-norm objective function to the reduced data set.32. A non-transitory computer readable medium storing a computerprogram, executable by a machine, for performing time domain channelestimation in a multi-user multiple input multiple output (“MIMO”)wireless network, the computer program comprising executableinstructions for: receiving data corresponding to transmission oftraining signals from a plurality of users to a base station over a MIMOwireless network; estimating a maximum delay spread for the receiveddata according to a coherence bandwidth of the received data;determining a limited data set by limiting the received data in a timedomain according to the estimated maximum delay spread; selecting anactive tap from the limited data set; determining a number of activetaps in the MIMO multi-user wireless network; forming a well-conditionedlow rank training matrix by identifying a channel model; estimating theactive tap from the formed well-conditioned low rank training matrix;and subtracting a contribution of the selected active tap from thelimited data set.